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5.3 Hydraulic Jump

The flow can change only from a supercritical flow to a subcritical flow, in which the height increases and the velocity decreases. There is no possibility for the flow to go in the reverse direction because of the Second Law of Thermodynamics (the explanation of which is out of the scope of this discussion). If there is no energy loss, the flow moves from point 1 to point 2 in Figure [*]. In actuality, energy loss occurs in any situation, but sometimes it can be neglected in the calculations. In cases where the flow changes rapidly (such as with the hydraulic jump), the energy loss must be taken into account. In these cases, the flow moves from point 1 to point 3 and has energy loss (). In many cases the change in the thrust is negligible, such as the case of the hydraulic jump, and the flow moves from point 1 to point 3 as shown in Figure [*].

In 1981, Garber ``found'' the hydraulic jump in the shot sleeve which he called a ``wave''. Garber built a model to describe this wave, utilizing mass conservation and Bernoulli's equation (energy conservation). This model gives a set of equations relating plunger velocity and wave velocity to other geometrical properties of the shot sleeve. Over 150 years earlier, Bélanger fluid:belanger demonstrated that the energy is dissipated, and that energy conservation models cannot be used to solve hydraulic jump. He demonstrated that the dissipation increases with the increase of the liquid velocity before the jump. This conclusion is true for any kind of geometry.

A literature review demonstrates that the hydraulic jump in a circular cross-section (like in a shot sleeve) appears in other cases, for example a flow in a storm sewer systems. An analytical solution that describes the solution is Bar-Meir's formula and is shown in Figure [*].

The energy loss concept manifests itself in several designs, such as in the energy-dissipating devices, in which hydraulic jumps are introduced in order to dissipate energy. The energy-dissipating devices are so common that numerous research works have been performed on them in the last 200 hundreds years. An excellent report by the U.S. Bureau of Reclamation [#!poro:bureau!#] shows the percentage of energy loss. However, Garber, and later other researchers from Ohio State University [#!poro:BrevickGarber!#], failed to know/understand/use this information.


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